Finite and infinite speed of propagation for porous medium equations with fractional pressure

2013/11/27 by Diana Stan, Félix del Teso, Stan, Diana +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1311.7007

openalex publication_date 2013/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a porous medium equation with fractional potential pressure: ∂_t u= ∇ ⋅ (u^m-1 ∇ p), p=(-Δ)^-su, for m>1, 00. The initial data u(x,0) is assumed to be a bounded function with compact support or fast decay at infinity. We establish existence of a class of weak solutions for which we determine whether, depending on the parameter m, the property of compact support is conserved in time or not, starting from the result of finite propagation known for m=2. We find that when m∈ [1,2) the problem has infinite speed of propagation, while for m∈ [2,∞) it has finite speed of propagation. Comparison is made with other nonlinear diffusion models where the results are widely different.

Citations

• Finite difference method for a general fractional porous medium equation

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